Fitting waggle dance models to waggle dance data

This document contains code to fit the waggle dance model to each of our 20 different sites. The code here uses the wagglefit package, as well as some additional code stored in fit_data.R to help simplify things here. Each site has its own section, with reused code. The final sections create map plots and summary statistic plots.

Optimising each site

In this document I have fit the collective and individual model to each site. So al the sites have reasonable likelihood values, however in some cases the fits are simply wrong (i.e. they show the probability of sampling a value greater than on equal to \(x\) as increasing in the tail). I need to trouble shoot these with Vincent. I also need to get some advice on how to plot the model fits to the histogram of data.

Would be a good idea to knit this as a single document / run in R studio on the laptop.

calc_dist_actual <- function(duration) {
  m = 1.38
  b = 0. #0.17
  distance = (duration-b) / m
  # distance = (1/m)*duration-(b/m)
  return(distance)
}

data <- read.csv("data/FullHBForagingData.csv")

head(data)

data$newforaging_distance <- calc_dist_actual(data$duration.seconds)

head(data)

par(mfrow = c(2, 2))
hist(data$duration.seconds)
hist(data$ForagingDistance_km)
hist(data$newforaging_distance)

min(data$newforaging_distance)

#> [1] 0.08695652

min(data$duration.seconds)

#> [1] 0.12

alldata <- data %>%
  select(date, site, newforaging_distance) %>%
  rename(foraging_distance = newforaging_distance)

BEL

Provides a good fit on the data. All parameters look central and nicely covered.

target_site <- "BEL"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 1.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 0.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 10, -5.5, -2)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

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all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
BEL	collective	-148.5623	0.6475794	7.041852	0.8144976	0.071051	0.2343415	5	307.1245	0.0980392	0.696
BEL	individual	-150.6485	1.0000000	4.500432	NA	0.100000	NA	2	305.2971	0.0882353	0.795

all_sites[[target_site]]$fit

BFI

All parameters look central in the likelihood space and a nice fit is returned.

target_site <- "BFI"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 0.6)
bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 4.5, -6.5, -2.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

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all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
BFI	collective	-116.7417	0.0444929	1e-06	2.762291	0.226579	0.3437162	5	243.4833	0.0873362	0.318
BFI	individual	-146.1395	1.0000000	1e+01	NA	0.100000	NA	2	296.2790	0.1266376	0.052

all_sites[[target_site]]$fit

BLO

The individual fit isnt great and the Bs paramater is increasing up to the boundry, indicating it can only really take on a straight line / exponential fit. The parameters for the collective model are fairly central in the likelihood space, the fit looks very good.

target_site <- "BLO"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-10, 5)
br_bnds <- c(1.0e-10, 5)
as_bnds <- c(1.0e-5, 5)
ar_bnds <- c(1.0e-10, 1.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 5505)
as_bnds <- c(1.0e-12, 0.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 12, -8., -2.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

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all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
BLO	collective	-166.2718	0.2085372	1.785832	0.570999	0.0934780	0.4955969	5	342.5435	0.0705882	0.775
BLO	individual	-182.6346	1.0000000	5505.000000	NA	0.0001686	NA	2	369.2692	0.1117647	0.218

all_sites[[target_site]]$fit

BUR

Bs and Br go in oposite directions. E.g. Bs approaches 0 whilst Br approaches an every higher number.

Fit looks good.

target_site <- "BUR"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 500)
br_bnds <- c(1.0e-6, 500)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 1.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 0.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 5.5, -6.5, -2.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

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all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
BUR	collective	-65.48321	0.111263	1e-06	499.5175	0.2080481	0.037952	5	140.9664	0.0670732	0.829
BUR	individual	-98.96132	1.000000	1e+01	NA	0.1000000	NA	2	201.9226	0.2134146	0.002

all_sites[[target_site]]$fit

CAD

The collective model roughly follows the individual model but is able to acheive a slightly improved fit to the shoulder, hence it provides a higher likelihood score. The AIC indicates this is overfitting, suggesting the individual model provides a more parsimonious explanation.

\(p\) does not approach 1 as one might expect, indicating there is overfitting and so a comparison with an individual model is required.

target_site <- "CAD"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 10)
ar_bnds <- c(1.0e-12, 10)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 2)
as_bnds <- c(1.0e-12, 0.8)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 2.5, -5, -1.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

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all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
CAD	collective	-24.76646	0.1641711	1e-06	0.4246688	2.0108993	0.5331572	5	59.53291	0.0821918	0.952
CAD	individual	-26.44103	1.0000000	1e-06	NA	0.5319316	NA	2	56.88206	0.1095890	0.733

all_sites[[target_site]]$fit

GIL

The collective model provides the most parsimonious and best fit.

target_site <- "GIL"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 1.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 0.8)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 2.7, -8., -2)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

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all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
GIL	collective	-12.70173	0.2599524	0.000001	1.71e-05	0.4619906	1.041126	5	35.40346	0.1354167	0.044
GIL	individual	-40.46915	1.0000000	2.036505	NA	0.4761262	NA	2	84.93831	0.1979167	0.000

all_sites[[target_site]]$fit

HER

The collective model provides the best fit to the data, but the proportion of scouts is high.

target_site <- "HER"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 100)
br_bnds <- c(1.0e-6, 100)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 1.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 2)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 5, -6.5, -1.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

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all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
HER	collective	-179.7794	0.6357164	0.0000010	1e-06	0.2448117	0.5938231	5	369.5588	0.1104651	0.220
HER	individual	-186.9235	1.0000000	0.5484173	NA	0.2520282	NA	2	377.8471	0.1395349	0.057

all_sites[[target_site]]$fit

HHS

Collective model provides the best fit but falls under the tail and shoulder. The individual model strugles to find a good fit, probably due to the tail.

target_site <- "HHS"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 50)
br_bnds <- c(1.0e-6, 50)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 1.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 6, -6.5, -2.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

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all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
HHS	collective	-32.36045	0.0954241	0.000001	1e-06	0.1947275	0.6940469	5	74.72089	0.1333333	0.364
HHS	individual	-54.76164	1.0000000	7.095172	NA	0.1727087	NA	2	113.52327	0.2444444	0.006

all_sites[[target_site]]$fit

HOR

Collective model provides a very good fit, whilst the individual model fails to find much traction. The proportion of scouts goes very low (~3%) suggesting the majority of the colony are following a small number of scouting individuals.

target_site <- "HOR"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 1.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 4, -9, -2.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

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all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
HOR	collective	-19.13936	0.0225268	0.000001	10	0.2939216	0.2794721	5	48.27872	0.0659898	0.333
HOR	individual	-86.68295	1.0000000	4.342541	NA	0.3515277	NA	2	177.36591	0.1852792	0.000

all_sites[[target_site]]$fit

MAK

Again the collective model provides a good fit to the data, however, the individual model fits poorly, reducing to an exponential.

target_site <- "MAK"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 20)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# run individual model
individual_result <- fit_individual_model_to_data(data, bounds)

#> [1] "Itteration 1"
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#> [1] "Itteration 10"

# view individual model likelihood space to check bounds look ok
individual_result$llspace

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 5, -6.5, -2.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
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#> [1] "Itteration 9"
#> [1] "Itteration 10"
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#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
MAK	collective	-52.69070	0.0641629	0.000001	10	0.1644266	0.1859693	5	115.3814	0.1010101	0.664
MAK	individual	-66.13831	1.0000000	9.168369	NA	0.1326216	NA	2	136.2766	0.1919192	0.038

all_sites[[target_site]]$fit

MEL

Collective model provides the best fit, however it misses a large section of the shoulder for the tail. The \(bs\) parameter wants to go to zero, however when let go bellow 1e-6 the behaviour becomes very erratic and the fit deteriorates.

target_site <- "MEL"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 3.5, -7, -2.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
MEL	collective	-75.70001	0.0801123	1e-06	1e-06	0.2942272	0.4661678	5	161.4000	0.1626016	0.060
MEL	individual	-96.11457	1.0000000	1e-06	NA	0.3478864	NA	2	196.2291	0.2439024	0.001

all_sites[[target_site]]$fit

MPA

Collective provides the best fit.

target_site <- "MPA"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 4.5, -7.2, -2.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
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#> [1] "Itteration 7"
#> [1] "Itteration 8"
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#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
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#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
MPA	collective	-133.7278	0.3583254	0.000001	1.952274	0.5793954	0.2263649	5	277.4557	0.06	0.941
MPA	individual	-139.7253	1.0000000	1.473854	NA	0.2575985	NA	2	283.4506	0.10	0.404

all_sites[[target_site]]$fit

ROT

Colletive provides the best fit.

target_site <- "ROT"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 3., -5.5, -2.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
ROT	collective	-76.30039	0	2.552248	0.7760085	0.0042611	0.4783701	5	162.6008	0.1185567	0.12
ROT	individual	-90.87080	1	0.000001	NA	0.4882476	NA	2	185.7416	0.2010309	0.00

all_sites[[target_site]]$fit

SAU

Collective provides the best fit.

target_site <- "SAU"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 3.5, -6.5, -2.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
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#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
SAU	collective	-65.66979	0.3090433	0.000001	10	0.3619172	0.2260465	5	141.3396	0.0606061	0.961
SAU	individual	-72.98751	1.0000000	1.488528	NA	0.3740337	NA	2	149.9750	0.1287879	0.194

all_sites[[target_site]]$fit

SOM

Collective provides the best fit but misses a large section of the shoulder.

target_site <- "SOM"

# subset data for target site
data <- alldata %>%
  filter(site == target_site) %>%
  filter(foraging_distance < 9) # remove outlier distance

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 3., -5.5, -2.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
SOM	collective	-42.18141	0.0142093	1e-06	10	0.1056866	0.2060172	5	94.36282	0.1061947	0.529
SOM	individual	-62.11560	1.0000000	1e+01	NA	0.1372393	NA	2	128.23120	0.2123894	0.008

all_sites[[target_site]]$fit

SRA

Collective provides the best fit.

target_site <- "SRA"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 4., -7.5, -2.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
SRA	collective	-74.62927	0.1338446	0.000001	9.99964	0.2800658	0.2024983	5	159.2585	0.0584416	0.940
SRA	individual	-88.51334	1.0000000	3.002015	NA	0.2944439	NA	2	181.0267	0.1428571	0.076

all_sites[[target_site]]$fit

STU

Individual provides the best fit. Again, the proportion of scouts does not move towards 1. I.e. the collective model fails to reduce to the individual in the MLE fit.

target_site <- "STU"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 10)
ar_bnds <- c(1.0e-12, 10)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 5.5, -6.5, -1.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
STU	collective	-93.23731	0.9909091	10.000000	10	0.0766245	5.290877	5	196.4746	0.0909091	0.730
STU	individual	-121.11113	1.0000000	1.346564	NA	0.2225088	NA	2	246.2223	0.0545455	0.995

all_sites[[target_site]]$fit

SWP

Collective provides the best fit.

target_site <- "SWP"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 15)
br_bnds <- c(1.0e-6, 15)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 2.5, -6, -2.)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
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#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
SWP	collective	-11.44422	0	3.251978	15	0.4581450	0.1883473	5	32.88845	0.1111111	0.629
SWP	individual	-17.45325	1	0.000001	NA	0.5846299	NA	2	38.90650	0.1444444	0.282

all_sites[[target_site]]$fit

YAL

Collective provides the best fit.

target_site <- "YAL"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 5., -8, -2.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
YAL	collective	-181.4945	0.1526265	0.9940565	0.2527173	0.2608775	0.395411	5	372.989	0.0646552	0.723
YAL	individual	-199.3440	1.0000000	0.5900944	NA	0.2941238	NA	2	402.688	0.0948276	0.245

all_sites[[target_site]]$fit

ZSL

Collective provides the best fit.

target_site <- "ZSL"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 50)
as_bnds <- c(1.0e-12, 1.3)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.5, 2.4, -8, -2)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
ZSL	collective	-23.05122	0.0512203	0.0000010	9.995463	0.5123196	0.2756678	5	56.10243	0.0481013	0.708
ZSL	individual	-54.51077	1.0000000	0.9650966	NA	0.5844393	NA	2	113.02154	0.1215190	0.005

all_sites[[target_site]]$fit

Overall findings

# group all site results together
df <- map(all_sites, 1) %>%
  bind_rows()

# save results
saveRDS(df, file = "results/site_fit_results.Rda")

# AIC plot
aic_plot <- df %>%
  group_by(site) %>%
  slice(which.min(AIC)) %>%
  select(model) %>%
  group_by(model) %>%
  summarise(lowest_AIC = n()) %>%
  ggplot(aes(x = model, y = lowest_AIC)) +
  geom_bar(stat = "identity") +
  labs(x = "Model", y = "Count") +
  scale_y_continuous(breaks = seq(0, 20, by = 2)) +
  theme(
    text = element_text(size = 42)
  )

ggsave(
  plot = aic_plot,
  filename = "results/figures/AIC_plot.png",
  width = 90,
  height = 110,
  units = "mm",
  dpi = 300
)

# ks plot
ks_plot_dist <- df %>%
  ggplot(aes(x = ks_pvalue)) +
  geom_histogram(bins = 10, binwidth = 0.1, col = "white") +
  geom_vline(xintercept = 0.05, color = "red", linetype = "dashed") +
  scale_y_continuous(breaks = seq(0, 12, by = 2)) +
  labs(x = "KS P value") +
  facet_wrap(~model, nrow = 3) +
  theme(
    text = element_text(size = 42),
    strip.background = element_blank()
  )


ggsave(
  plot = ks_plot_dist,
  filename = "results/figures/sites_ks.png",
  width = 86,
  height = 180,
  units = "mm",
  dpi = 300
)

ggsave(
  plot = all_sites$STU$fit,
  filename = "results/figures/STU.png",
  width = 90,
  height = 110,
  units = "mm",
  dpi = 300
)

ggsave(
  plot = all_sites$ZSL$fit,
  filename = "results/figures/ZSL.png",
  width = 90,
  height = 110,
  units = "mm",
  dpi = 300
)

Map plots

Code to make the individual mal plots. These figures are created standalone but are combined in to facets manually in an image processor.

library(ggplot2)
library(ggrepel)
library(gridExtra)
library(ggsn)
library(sf)
library(rworldmap)
library(ggspatial)
library(rnaturalearth)
library(rnaturalearthdata)


full_data_path <- "data/FullHBForagingData.csv"
data_raw <- tibble(read.csv(full_data_path))

map_data <- data_raw %>%
  select(
    site, lat, lon
  ) %>%
  distinct()

map_data <- df %>%
  group_by(site) %>%
  slice(which.min(AIC)) %>%
  select(site, model) %>%
  left_join(map_data, on = "site") %>%
  mutate(col = ifelse(site %in% c("STU", "ZSL"), "1", "0"))

locations <- st_as_sf(
  map_data,
  coords = c("lon", "lat"), crs = 4326
)

# Extract selected sites for figure
selected_sites <- filter(map_data, site %in% c("STU", "ZSL")) %>%
  mutate(
    label = ifelse(site == "STU", "C (STU)", "D (ZSL)")
  )

points_area <- st_bbox(locations)

worldmap <- ne_countries(scale = "large", returnclass = "sf")

# london area
london <- st_read(
  "shapefiles/London_Ward.shp"
)

#> Reading layer `London_Ward' from data source 
#>   `/home/joe/Documents/PhD/wagglefit/analysis/shapefiles/London_Ward.shp' 
#>   using driver `ESRI Shapefile'
#> Simple feature collection with 649 features and 0 fields
#> Geometry type: POLYGON
#> Dimension:     XY
#> Bounding box:  xmin: 503568.2 ymin: 155850.8 xmax: 561957.5 ymax: 200933.9
#> Projected CRS: OSGB 1936 / British National Grid

london <- st_transform(
  london,
  CRS("+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0")
)

inset <- ggplot() +
  geom_sf(
    data = worldmap,
    fill = "grey90",
    color = "#4b4949d0"
  ) +
  geom_sf(
    data = london,
    fill = "#ced0cffc",
    lwd = 0
  ) +
  coord_sf(
    xlim = c(points_area[[1]] - 0.1, points_area[[3]] + 0.1),
    ylim = c(points_area[[2]] - 0.1, points_area[[4]] + 0.1)
  ) +
  geom_point(
    data = map_data,
    aes(x = lon, y = lat, shape = model, colour = model), size = 1.5
  ) +
  geom_text(
    data = selected_sites, aes(x = lon, y = lat, label = label),
    nudge_x = c(0, -0.07), nudge_y = c(0.05, 0.05), size = 8
  ) +
  annotation_north_arrow(
    location = "tr", which_north = "true",
    style = north_arrow_fancy_orienteering,
    height = unit(15, "mm"),
    width = unit(15, "mm"),
    text_cex = 1.5
  ) +
  annotation_scale(
    location = "br",
    text_cex = 1.5
  ) +
  scale_shape_manual(values = c(1, 2)) +
  scale_colour_manual(values = c("black", "red")) +
  theme_nothing() +
  scale_x_continuous(expand = c(0, 0)) +
  scale_y_continuous(expand = c(0, 0)) +
  labs(x = NULL, y = NULL) +
  theme(
    panel.border = element_rect(color = "black", fill = NA, size = .5)
  )

inset

# make full plot
base <- ggplot(data = worldmap) +
  geom_sf(
    fill = "#c4cfc8",
    color = "#4b4949d0",
    lwd = 0.2
  ) +
  coord_sf(
    xlim = c(-11, 3),
    ylim = c(49.5, 60)
  ) +
  # geom_point(data = map_data, aes(x = lon, y = lat), size = 0.2) +
  geom_rect(
    aes(
      xmin = points_area$xmin[[1]] - 0.1, xmax = points_area$xmax[[1]] + 0.1,
      ymin = points_area$ymin[[1]] - 0.1, ymax = points_area$ymax[[1]] + 0.1
    ),
    fill = NA,
    colour = "black",
    size = .02
  ) +
  theme_nothing() +
  scale_x_continuous(expand = c(0, 0)) +
  scale_y_continuous(expand = c(0, 0)) +
  labs(x = NULL, y = NULL) +
  theme(
    panel.border = element_rect(color = "black", fill = NA, size = .5)
  )

base

merge_plot <- base +
  annotation_custom(
    ggplotGrob(inset),
    xmin = 1,
    xmax = 13,
    ymin = 52.5,
    ymax = 60
  )

merge_plot

ggsave(
  plot = merge_plot,
  filename = "results/figures/site_map.png",
  width = 90,
  height = 110,
  units = "mm",
  dpi = 300
)


merge_plot_2 <- inset +
  annotation_custom(
    ggplotGrob(base),
    xmin = -3.35,
    xmax = 2,
    ymin = 51.05,
    ymax = 51.35
  )

merge_plot_2

sites_model_plot <- plot_grid(
  merge_plot_2, ks_plot_dist, all_sites$STU$fit, all_sites$ZSL$fit,
  labels = c("A", "B", "C", "D"), label_size = 24
)

ggsave(
  plot = sites_model_plot,
  filename = "results/figures/sites_model_plot.png",
  width = 183,
  height = 190,
  units = "mm",
  dpi = 300
)

model_sites_fits <- plot_grid(
  merge_plot_2, ks_plot_dist,
  labels = c("A", "B"), label_size = 24
)

ggsave(
  plot = model_sites_fits,
  filename = "results/figures/model_sites_fits.png",
  width = 183,
  height = 190,
  units = "mm",
  dpi = 300
)

stu_zsl_fit <- plot_grid(
  all_sites$STU$fit, all_sites$ZSL$fit,
  labels = c("A", "B"), label_size = 24
)

ggsave(
  plot = stu_zsl_fit,
  filename = "results/figures/stu_zsl_fit.svg",
  width = 183,
  height = 190,
  units = "mm",
  dpi = 100
)

# other map plots
inset <- ggplot() +
  geom_sf(
    data = worldmap,
    fill = "grey90",
    color = "#4b4949d0"
  ) +
  geom_sf(
    data = london,
    fill = "#ced0cffc",
    lwd = 0
  ) +
  coord_sf(
    xlim = c(points_area[[1]] - 0.1, points_area[[3]] + 0.1),
    ylim = c(points_area[[2]] - 0.1, points_area[[4]] + 0.1)
  ) +
  geom_point(
    data = map_data,
    aes(x = lon, y = lat, shape = model, colour = model), size = 1.5
  ) +
  annotation_north_arrow(
    location = "tr", which_north = "true",
    style = north_arrow_fancy_orienteering,
    height = unit(10, "mm"),
    width = unit(10, "mm")
  ) +
  annotation_scale(
    location = "br",
    text_cex = 3
  ) +
  scale_shape_manual(values = c(1, 2)) +
  scale_colour_manual(values = c("black", "red")) +
  theme_nothing() +
  scale_x_continuous(expand = c(0, 0)) +
  scale_y_continuous(expand = c(0, 0)) +
  labs(x = NULL, y = NULL) +
  theme(
    panel.border = element_rect(color = "black", fill = NA, size = .5),
    text = element_text(size = 42)
  )

inset

# make full plot
base <- ggplot(data = worldmap) +
  geom_sf(
    fill = "#c4cfc8",
    color = "#4b4949d0",
    lwd = 0.2
  ) +
  coord_sf(
    xlim = c(-11, 15),
    ylim = c(49.5, 60)
  ) +
  geom_point(data = map_data, aes(x = lon, y = lat), size = 0.2) +
  geom_rect(
    aes(
      xmin = points_area$xmin[[1]] - 0.1, xmax = points_area$xmax[[1]] + 0.1,
      ymin = points_area$ymin[[1]] - 0.1, ymax = points_area$ymax[[1]] + 0.1
    ),
    fill = NA,
    colour = "black",
    size = .02
  ) +
  theme_nothing() +
  scale_x_continuous(expand = c(0, 0)) +
  scale_y_continuous(expand = c(0, 0)) +
  labs(x = NULL, y = NULL) +
  theme(
    panel.border = element_rect(color = "black", fill = NA, size = .5)
  )

merge_plot <- base +
  annotation_custom(
    ggplotGrob(inset),
    xmin = 1,
    xmax = 13,
    ymin = 52.5,
    ymax = 60
  )

merge_plot

ggsave(
  plot = merge_plot,
  filename = "results/figures/site_map.png",
  width = 183,
  height = 190,
  units = "mm",
  dpi = 300
)


sites_model_plot <- plot_grid(
  all_sites$STU$fit, all_sites$ZSL$fit, aic_plot, ks_plot_dist,
  labels = c("A", "B", "C", "D"), label_size = 42
)

sites_model_plot

ggsave(
  plot = sites_model_plot,
  filename = "results/figures/results_model_plot.png",
  width = 183,
  height = 190,
  units = "mm",
  dpi = 300
)